1. Given the vectors a, b, and c. It is necessary to: a) calculate the mixed product of three vectors; b) Find the unit vector product; c) to calculate the inner product of two vectors; g) check whether collinear or orthogonal two vectors; e) verify whether the three vectors are coplanar.
1.22 a = 7i - 4j - 5k, b = i - 11j + 3k, c = 5i + 5j + 3k; a) 3a, -7b, 2c; b) 2b, 6c; in) -4a, -5c; g) a, c; d) -4a, 2b, 6c.
2. The top of the pyramid are located at points A, B, C and D. Calculate: a) the area of the said faces; b) cross-sectional area, passing through the middle of the rib l and two top of the pyramid; c) the volume of the pyramid ABCD.
2.22 A (-2, -5, -1), B (-6, -7, 9), C (4, -5, 1), D (2, 1, 4); a) BCD; b) l = BC, A and D
3. Given three powers P, Q, R, applied to point A. Calculate: a) work done by the resultant of these forces, when the point of its application, moving rectilinearly moves to point B; b) the amount of time the resultant of these forces about point B.
3.22 P = (7, 3, -4), Q (9, -4, 2), R (-6, 1, 4), A (-7, 2, 5), B (4, -2, 11, )